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Although various investigations of Atkinson cycle have been carried out, distinct output power and thermal efficiencies of the engine have been achieved. In this regard, thermal efficiency, Ecological Coefficient of Performance (ECOP), and Ecological function (ECF) are optimized with the help of NSGA-II method and thermodynamic study.  The Pareto optimal frontier which provides an ultimate optimum solution is chosen utilizing various decision-making approaches, containing fuzzy Bellman-Zadeh, LINMAP, and TOPSIS. With the help of the results, interpreting the performances of Atkinson cycles and their optimization is enhanced. Error analysis has also been performed for verification of optimization and determining the deviation in the study.